Sample Methodologies for Regional Emissions Analysis in Small Urban and Rural Areas

Appendix

Appendix
Parameters and Defaults Values for Use with the BPR Formula for Estimating Speed

As described in Section 3, use of the BPR-type formulas (and other methods) requires three inputs: free-flow speed, roadway capacity, and traffic volume. Traffic volume information is developed as described in Section 2 of this report. The accuracy of this method is highly dependent on the accuracy of the capacity and free-flow speed inputs. This appendix described in detail the procedures for developing these two inputs, including default parameter values and some examples.

When using these equations to estimate free-flow speed on a large number of links, it is typically impractical to apply the equations individually for each link. Instead, the equations are used to develop look-up tables of free-flow speeds by facility type and area type. The look-up table is then used to quickly assign free-flow speeds to each link. Below is an example if such a look-up table.

Example - Look-up table of default free-flow speeds (mph)

Free-flow speeds (mph)

Freeway

Expressway

Arterial

Collector

Local

CBD

50

45

40

35

30

Urban

55

50

45

40

35

Suburban

60

55

50

45

40

Rural

65

60

55

50

45

Source: Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications,

NCHRP Report 387, Transportation Research Board, 1997.

Free-flow speeds can be determined using other more simplistic methods. Some regions estimate flow speeds by facility type based on the posted speed limit, such as adding or subtracting a fixed amount to/from the speed limit (e.g., speed limit plus 5 mph for highways) or multiply the speed limit by a fixed percentage (e.g., 62% of speed limit for collectors). These simple adjustments to posted speed limits are usually based on a limited sample of measured local speeds that are available for the desired roadway classification. When using these rules for estimating free-flow speeds, the equations often differ based on area type (e.g., CBD, rural, etc.). Other regions estimate free-flow speeds by facility type using observed off-peak speeds.

Roadway capacity estimation

NCHRP Report 387 recommends a set of equations for estimating capacity that are based on the 1994 Highway Capacity Manual. There are separate equations for freeways, 2-lane unsignalized roads, and signalized arterials.

Capacity equation for freeways and unsignalized multilane roads:

Capacity (vph) = Ideal Cap * N * Fhv * PHF

Where:

Ideal Cap = 2,400 (pcphl) for freeways with >=70 mph free-flow speed

= 2,300 (pcphl) for all other freeways (free-flow speed < 70 mph)

N = number of through lanes (Ignore auxiliary lanes and "exit only" lanes)

Fhv = heavy vehicle adjustment factor

= 100/(100 + 0.5 * HV) for level terrain

= 100/(100 + 2.0 * HV) for rolling terrain

= 100/(100 + 5.0 * HV) for mountainous terrain

(HV = proportion of heavy vehicles, including trucks, buses, recreational vehicles, in the traffic flow. If HV is unknown, use 0.05 heavy vehicles as default.)

= 1.10 if exclusive left turn lanes (often as left turn bay) are present

= 1.00 otherwise

FCBD = central business district adjustment factor

= 0.90 if located in CBDs

= 1.00 elsewhere

g/C = ratio of effective green time per cycle

If no data are available, use the following defaults:

Protected left turn phase present: g/C = 0.40

Protected left turn phase not present: g/C = 0.45

Other defaults may be developed by the local planning agency based on local conditions. Additional defaults might be based on the functional class of major and crossing streets.

Fc = optional user-specified calibration factor necessary to match estimated capacity with field measurements or other independent estimates of capacity (no units) (can be used to account for the capacity-reducing effects of left and right turns made from through lanes)

As with free-flow speeds, it is usually impractical to apply the capacity equations individually for every link, so look-up tables are developed.

If traffic volume data is on a daily basis (AADT), then hourly capacity must be converted to an effective daily capacity. In one approach to calculate 24-hour capacity, the hourly capacity per lane is divided by the ratio of AADT that occurs in the peak hour. This figure is then multiplied by the number of lanes in the peak direction, and in the off peak direction is multiplied by the number of lanes and a directional adjustment factor. A 24-hour volume-to-capacity (V/C) ratio is then calculated by dividing AADT by 24-hour capacity.

Construction of a Localized Capacity Look-Up Table

Because the accuracy of capacity estimates is essential to the accuracy of speed estimates, NCHRP Report 387 recommends that planning agencies use the specific capacities of the selected study section. When that is not possible, the following tables demonstrate the procedure for selecting default values and computing a look-up table of capacities, according to facility, area, and terrain type. The first table is for two-lane, rural undivided arterials, but additional rows of data could be added for multilane rural undivided arterials. The second table provides a sample computation.

Many regions have modified the parameters a and b so that the formula calculates speeds that more closely reflect observed local speeds. The original BPR formula uses a = 0.15 and b = 4. Other regions have used values of a as high as 1.0 and values of b as high as 11.

Advantages

Able to produce highly accurate speed estimates if applied properly.

Accounts for future congestion impacts on speed.

Limitations

In order to produce accurate speed results, requires accurate local information on capacity and free-flow speed. Use of default look-up tables for these values often leads to inaccurate speed estimates.

Ohio DOT used the original form of the BPR formula (a = 0.15 and b = 4) to estimate speed in rural areas not covered by a TDF model. To estimate free-flow speeds, Ohio DOT used the upper bound of the table provided in the HCM for each functional class.